Quantum Wave Function VisualizationYouTube↗  IA↗(long shot)
Science & Technology  789K views 13.8K likes 267 dislikes   13 Feb 2016
Physics Videos by Eugene Khutoryansky 1M subscribers United States YouTube↗


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According to Quantum Mechanics,
根据量子力学，
all particles in the Universe are described by what we call a wave function.
宇宙中的所有粒子都被我们称之为波函数的东西描述。
Properties such as position and momentum
位置和动量等属性
do not have defined values until they are observed.
在观察之前没有定义的值。
The probability of each possible observation is determined by the wave function.
每个可能观察的概率由波函数确定。
Suppose we have a particle moving freely through space in one dimension.
假设我们有一个粒子在一个维度上自由地穿过空间。
Its wave function may look as shown.
其波函数可能如图所示。
The probability of the particle being at a particular position is given by
粒子处于特定位置的概率由下式给出
the square of the amplitude of the wave function at that location.
该位置的波函数幅度的平方。
Now let us consider a particle that is moving in one dimension,
现在让我们考虑一个在一个维度上移动的粒子，
but is trapped inside a box.
但被困在一个盒子里面。
Its wave function may look as shown.
其波函数可能如图所示。
At each point in space and time, all wave functions are described by a complex number.
在空间和时间的每个点，所有波函数都由复数描述。
All complex numbers have a real component and an imaginary component.
所有复数都有一个实数组件和一个虚构组件。
A particle with a higher energy will have a wave function
具有较高能量的粒子将具有波函数
that rotates with a higher frequency, and it will look like this.
以更高的频率旋转，它看起来像这样。
The wave function can also be in a combination of this waveform and the previous one.
波函数也可以是该波形与前一波形的组合。
We say that this wave function is in a superposition
我们说这个波函数是叠加的
of the two wave functions we saw earlier.
我们之前看到的两个波函数。
Since this waveform is a combination of two different wave functions
由于该波形是两种不同波函数的组合
with different energy levels, the energy of this particle is uncertain.
在不同的能量水平下，这种粒子的能量是不确定的。
When we measure the energy,
当我们测量能量时，
we say that the wave function collapses into one of the two original wave functions.
我们说波函数折叠成两个原始波函数之一。
The wave function’s frequency determines the particle’s energy.
波函数的频率决定了粒子的能量。
The momentum of the particle is determined by the wave function’s wavelength.
粒子的动量由波函数的波长决定。
A longer wavelength implies a smaller momentum.
较长的波长意味着较小的动量。
In this scenario, we have a particle moving freely through space with a known momentum.
在这种情况下，我们有一个粒子在已知动量的空间中自由移动。
However, the position of the particle is completely unknown,
然而，粒子的位置是完全未知的，
because the amplitude of the wave function is the same everywhere.
因为波函数的幅度在各处都是相同的。
The square of the amplitude of the wave function at each location
每个位置的波函数幅度的平方
determines the probability of measuring the particle at that location.
确定在该位置测量粒子的概率。
We can have some knowledge of the particle’s location
我们可以对粒子的位置有一些了解
if the wave-function consists of the sum of several different waveforms
如果波函数由几个不同波形的总和组成
with different wavelengths.
具有不同的波长。
In this case, we have more knowledge of the particle’s location,
在这种情况下，我们对粒子的位置有了更多的了解，
since the amplitude of the wave function is larger in one area.
因为波函数的幅度在一个区域中较大。
But, we now have less knowledge of the particle’s momentum,
但是，我们现在对粒子动量的了解不多，
since the wave function is composed of waveforms of different wavelengths.
由于波函数由不同波长的波形组成。
If we measure the momentum precisely,
如果我们准确地测量动量，
then the wave function will collapse into one of these waveforms,
然后波函数将折叠成其中一个波形，
and we will again have no knowledge of the particle’s position.
我们将再一次不知道粒子的位置。
The more knowledge we have about the particle’s momentum,
我们对粒子动量的了解越多，
the less knowledge we have about the particle’s position.
我们对粒子位置的了解越少。
And the more knowledge we have about the particle’s position,
我们对粒子位置的了解越多，
the less knowledge we have about the particle’s momentum.
我们对粒子动量的了解越少。
This is because
这是因为
the more we want to limit the wave function’s peak in amplitude to one narrow location,
我们越想将波函数的幅度峰值限制在一个狭窄的位置，
the greater the number of different wavelengths we will have to add together.
我们必须加在一起的不同波长的数量越多。
Note that the velocity of the particle is not the velocity of any of the
请注意，粒子的速度不是任何单独波形图的速度，
individual waveforms, but the velocity of the pattern that forms
out of the sum of all of the waveforms that make up the total wave function.
而是构成总波函数的所有波形总和的波形图的速度。
When a particle is traveling freely through space,
当粒子在太空​​中自由行进时
there are no limitations to a wave-function’s possible wavelength and frequency.
波函数可能的波长和频率没有限制。
On the other hand, if a particle is trapped inside a box,
另一方面，如果粒子被困在盒子里面，
the only wavelengths and frequencies that are possible are the ones that ensure
可能的唯一波长和频率是确保的
that the amplitude of the wave function is close to zero at the boundary of the box.
波函数的幅度在框的边界处接近于零。
This means that for a trapped particle, waveforms in between these frequencies
这意味着对于被捕获的粒子，这些频率之间的波形
are not allowed, and hence only certain energy levels are possible.
是不允许的，因此只有一定的能量水平是可能的。
At each point in space and time, the wave function is described by a complex number
在空间和时间的每个点处，波函数由复数描述
which has a real component and an imaginary component.
它有一个真实的组件和一个虚构的组件。
In order to help visualize the upcoming explanations,
为了帮助想象即将到来的解释，
let us just show the real component of the wave-function.
让我们只展示波函数的真实成分。
So far, we have only been talking about particles moving in one dimension.
到目前为止，我们只讨论过在一个维度上移动的粒子。
Now, let us consider a particle moving in two dimensions.
现在，让我们考虑一个二维移动的粒子。
Amplitude must always be close to zero along all four edges.
沿所有四个边缘的幅度必须始终接近零。
If the particle is trapped inside a box,
如果粒子被困在盒子里面，
then only certain energy levels will be possible in each of the two dimensions.
那么在两个维度中的每个维度中只能有一定的能量水平。
The frequency in each of the two dimension indicates the energy in that dimension.
两个维度中的每个维度中的频率表示该维度中的能量。
Energy must be present in both dimensions to ensure zero amplitude at the edges.
必须在两个维度上存在能量以确保边缘处的零振幅。
Now let us consider a particle called an electron, moving in three dimensions,
现在让我们考虑一个叫做电子的粒子，在三维空间中移动，
trapped by the electrical attraction of an atomic nucleus.
陷入原子核的电吸引力。
As in the previous examples,
与前面的例子一样，
only certain energy levels for the electron will be possible.
只有某些电子能级才有可能。
The wave functions with specific energy levels that are possible
波浪具有可能的特定能量水平
are what we refer to as the electron orbitals of an atom.
是我们所说的原子的电子轨道。
Much more information on Quantum Mechanics
关于量子力学的更多信息
is available in the other videos on this channel.
可在此频道的其他视频中找到。
Please subscribe for notifications when new videos are ready.
新视频准备就绪时，请订阅通知。
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